Fiberings into analytic curves

In this paper we study fiberings of analytic manifolds (mainly, Stein manifolds) into analytic curves. The leading special case is a fibering into solutions of the differential equation $\dot z=F(z)$, $z\in\mathbf C^n$, with the right side entire analytic. We introduce two geometrical objects connected with a fibering: the manifold $\widehat\Phi$ of coverings of fibers and the domain of preservation of cycles $\Omega$. The main theorem asserts that under some general assumptions the manifold $\widehat\Phi$ is a Stein manifold. Under the same assumptions the domain $\Omega$ is a Stein space.
Figures: 4.
Bibliography: 7 titles.